Question

In 1979, the price of electricity was $0.05 per kilowatt-hour. The price of electricity has increased at a rate of approximately 2.05% annually. If t is the number of years after 1979, create the equation that can be used to determine how many years it will take for the price per kilowatt-hour to reach $0.10. Fill in the values of a, b, and c for this situation. Do not include dollar signs in the response.

Answer 1

The equation would be

$0.10=0.05(1+0.0205)^t$

and it would take 34.16 years.

0.10 is the amount we're trying to get; 0.05 is the initial value; and 0.0205 is the percent of increase, 2.05%, written as a decimal number.

To evaluate, we combine everything in parentheses:
$0.10=0.05(1.0205)^t$

Divide both sides by 0.05:
$\frac{0.10}{0.05}=\frac{0.05(1.0205)^t}{0.05} \\ \\2=1.0205^t$

We solve this using a logarithm:

$\log_{1.0205}2=t \\ \\34.16=t$